| Summary: | Single (one-dimensional) and bi-cubic (two-dimensional) splines have been used in numerical weather prediction models since about 1970. Especially the semi-Lagrangian advection schemes have been developed with the help of the spline interpolation method. In this paper the consequent formulation of a primitive equation grid point model with bi-cubic splines is investigated. Numerical experiments show that the complete replacement of all horizontal finite difference approximations in the advective and non-advective terms by the associated bi-cubic splines leads to a minor increase of forecast quality, which is accompanied by an inappropriate and uneconomical increase of computing time. With respect to the semi-Lagrangian treatment of the horizontal advection problem, split explicit schemes with single cubic splines produce a slightly reduced forecast quality compared with the more complex bi-cubic splines. Because on the other hand the numerical costs are not raised by the two-dimensional advection method, the use of the physically more reasonable bi-cubic spline interpolation is recommended.
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